Riya Plans to Order 95 Custom Shirts

Question

Riya plans to order 95 custom shirts for the participants of a fundraising event she is organizing. She is considering two options for ordering the shirts—a local option where she would have no shipping costs and an option to order the shirts online and have them shipped to her. If she uses the local option, each shirt will cost $x. If she uses the online option, each shirt will cost slightly less, at $y, but she will have to pay a flat shipping fee of $22. These are the only costs associated with ordering the shirts. Riya correctly determined that by ordering the 95 shirts using the online option rather than the local option, she will spend exactly $16 less.

Select a value for x and a value for y that are jointly consistent with the information provided. Make only two selections, one in each column.

chetan2u · Accepted Answer

Let us work out the cost under both options.

Local Option : 0$(shipping cost) + $95x(at the rate of $x per shirt)
 Onlne Option : 22$(shipping cost) + $95y(at the rate of $y per shirt), where y<x

Local cost - Online cost = $16
95x-(22+95y)=16
95(x-y)=38
x-y = 38/95 = 0.4
 Look for options that have a difference of 0.4 => 12.50-12.10 
 Thus, x=12.50 and y=12.10

JoeKan1234 · Answer

First, understand the problem and formulate an equation:

95y + 22 = 95x - 16

This means...

38 = 95 (x-y)

2*19 = 5*19(x-y)

2 = 5*(x-y)

Notice that x-y is not an integer.

Since 2 is an integer, x-y must be divisible by 5.

Let's try the decimals that end with 0 because they seem to be divisible by 5, namely 12.50 and 12.10.

Let's assume x = 12.50, y = 12.10, then x-y = 12.50 - 12.10 = 0.4 = 2/5

Bingo, (2/5)*5 = 2

So the assumption is correct

Rohanx9 · Answer

Logical way to do it without algebra:

If ordered online, she saves $16, despite paying $22 extra for shipping. Therefore she pays $16 + $22 = $38 less for the 95 shirts if ordered online.

That means each shirt would cost $38 / 95 = $0.4 less per shirt. I.e. difference between prices is 0.4.

Find two values that have a difference of 0.4, and X will be the larger one of the two.

Only X = $12.10 and Y = $12.50 fit.

HarshavardhanR · Answer

Cost (Local) = 95x
Cost (Online) = 95y + $22 (shipping)

Given: 95x - (95y+22) = 16

=> 95 (x - y) = 38
=> x - y = 0.4

Now, looking at the choices ->  x=12.50  and  y=12.10

Harsha

x	y
		12.04
		12.10
		12.25
		12.33
		12.50

Riya Plans to Order 95 Custom Shirts

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